Harnack inequality for the linearized

parabolic Monge-Ampère equation

Author:
Qingbo Huang

Journal:
Trans. Amer. Math. Soc. **351** (1999), 2025-2054

MSC (1991):
Primary 35K10; Secondary 35B45

DOI:
https://doi.org/10.1090/S0002-9947-99-02142-X

Published electronically:
January 27, 1999

MathSciNet review:
1467468

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove the Harnack inequality for nonnegative solutions of the linearized parabolic Monge-Ampère equation

on parabolic sections associated with , under the assumption that the Monge-Ampère measure generated by satisfies the doubling condition on sections and the uniform continuity condition with respect to Lebesgue measure. The theory established is invariant under the group , where denotes the group of all invertible affine transformations on .

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Additional Information

**Qingbo Huang**

Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Address at time of publication:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Email:
qhuang@math.utexas.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02142-X

Keywords:
Harnack inequality,
affine invariant,
linear parabolic Monge-Amp\`{e}re equation,
section

Received by editor(s):
December 15, 1996

Received by editor(s) in revised form:
May 13, 1997

Published electronically:
January 27, 1999

Article copyright:
© Copyright 1999
American Mathematical Society